Is it possible to fake a specific path for a process?

LD_PRELOAD isn't too difficult, and you don't need to be root. Interpose your own C routine which is called instead of the real open() in the C library. Your routine checks if the file to open is "/tmp/adb.log" and calls the real open with a different filename. Here's your shim_open.c:

/*
 * capture calls to a routine and replace with your code
 * gcc -Wall -O2 -fpic -shared -ldl -o shim_open.so shim_open.c
 * LD_PRELOAD=/.../shim_open.so cat /tmp/adb.log
 */
#define _FCNTL_H 1 /* hack for open() prototype */
#define _GNU_SOURCE /* needed to get RTLD_NEXT defined in dlfcn.h */
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <dlfcn.h>
#define OLDNAME "/tmp/adb.log"
#define NEWNAME "/tmp/myadb.log"

int open(const char *pathname, int flags, mode_t mode){
    static int (*real_open)(const char *pathname, int flags, mode_t mode) = NULL;

    if (!real_open) {
        real_open = dlsym(RTLD_NEXT, "open");
        char *error = dlerror();
        if (error != NULL) {
            fprintf(stderr, "%s\n", error);
            exit(1);
        }
    }
    if (strcmp(pathname,OLDNAME)==0) pathname = NEWNAME;
    fprintf(stderr, "opening: %s\n", pathname);
    return real_open(pathname, flags, mode);
}

Compile it with gcc -Wall -O2 -fpic -shared -ldl -o shim_open.so shim_open.c and test it by putting something in /tmp/myadb.log and running LD_PRELOAD=/.../shim_open.so cat /tmp/adb.log. Then try the LD_PRELOAD on adb.

Here is a very simple example of using util-linux's unshare to put a process in a private mount namespace and give it a different view of the same filesystem its parent currently has:

{   cd /tmp                      #usually a safe place for this stuff
    echo hey   >file             #some
    echo there >file2            #evidence
    sudo unshare -m sh -c '      #unshare requires root by default
         mount -B file2 file     #bind mount there over hey
         cat file                #show it
         kill -TSTP "$$"         #suspend root shell and switch back to parent
         umount file             #unbind there
         cat file'               #show it
    cat file                     #root shell just suspended
    fg                           #bring it back
    cat file2                    #round it off
}

---

there                            #root shell
hey                              #root shell suspended
hey                              #root shell restored
there                            #rounded

You can give a process a private view of its filesystem with the unshare utility on up-to-date linux systems, though the mount namespace facility itself has been fairly mature for the entire 3.x kernel series. You can enter pre-existing namespaces of all kinds with nsenter utility from the same package, and you can find out more with man.